It’s not uncommon to hear the advice that entrepreneurs should take more calculated risks if they want to be successful. In fact, some billionaires have built their personal brands on a foundation of risk; as an example, Richard Branson often speaks of the risks he took when he was young, and he encourages up-and-comers to do the same.

Taking risks, in fact, can be a beneficial way to separate yourself from the pack. If the fear of failure is holding back your peers, your willingness to take a risk could give you an open, uncontested opportunity. In addition, risky decisions offer valuable lessons, regardless of whether you succeed or fail.

But does risk-taking, in general, lead to success? The answer depends on the following factors:

The importance of "calculated" risk-taking

First, it’s important to note that open risk-taking generally isn't productive. Instead, successful entrepreneurs tend to take risks in ways that limit their potential losses. As Leonard C. Green pointed out, in Entrepreneur, "Entrepreneurs are not risk-takers. They are calculated risk takers.

"The difference between risk-takers and calculated risk-takers is the difference between failure and success," Green said.

In other words, calculated risk-takers might not play a game of roulette, because the odds are against them, yet they might be open to playing blackjack because it’s possible in that game to tip the odds in your favor through strategic play.

The importance of "survivorship bias"

Still, what are we to make of all the successful entrepreneurs who credit at least a portion of their success to risk? The evidence they cite often isn’t good enough to illustrate the effects of risk-taking, because we are left susceptible to survivorship bias.

Some observers suggested studying the planes that returned home and ooking at their bullet patterns, then providing armor in the areas of the plane that had been most heavily shot -- since these were the areas where a plane was most likely to get hit.

Wald offered a dissenting opinion. He suggested coating the areas of planes that corresponded with untouched areas on returning planes. There was no available sample for planes that had been shot down, and returning planes proved which areas of a plane could be shot without necessarily destroying the plane.

The difference between "risk" vs. "uncertainty"

We also need to consider the difference between what we conceive of as constituting “risk” versus what we describe as “uncertainty.” Both concepts describe a situation with an unknown outcome, but in the words of economist Frank Knight, “The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character.

Continued Knight: "There are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.”

You can think of risk as a distribution of known probabilities. If you shuffle a standard deck of playing cards, you know your chances of drawing the king of hearts will be 1 in 52. The chances of drawing any heart card will be 1 in 4. You can calculate the other probabilities from there, and place bets in a way that aligns with the risk you’re taking.

Where uncertainty comes in is when you’re dealing with unknown probability distributions. Think about watching someone assemble cards randomly, from different decks, until that person has a new deck of 52 cards. There could be 52 kings of hearts in there! Or 51 standard playing cards with an extra 10 of clubs! Or anything in between, for that matter.

By this definition, successful entrepreneurs tend to be those who seek uncertainty, rather than risk. They aren’t building businesses that have a 25 percent chance of success; they’re building businesses where the chance of success is more ambiguous.

The bottom line

The bottom line here is that risk-taking does have some correlation with success, but there are too many complicating factors to say that risk-taking increases your chances of success. Survivorship bias, meanwhile, distorts our perspective on the role that risk plays in success. Furthermore, we use inconsistent terminology to describe the differences between uncertainty and risk.

So, ultimately, even the best and boldest entrepreneurs need to find ways to mitigate damage from the risks they take.